Geodesic
An object moving in $\mathbb R^2$ with a high-speed destructive miniobject and an unfriendly solid observer
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 26 (2020) no. 4, pp. 76-82 Cet article a éte moissonné depuis la source Math-Net.Ru

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We propose a model for the motion in a given corridor $Y\subset \mathbb{R}^2$ of an object $t$ equipped with a high-speed destructive miniobject in the presence of a solid unfriendly observer $f$. In $\mathbb{R}^2\backslash Y$ there is a subset $G$ that obstructs visibility and motion. For safety reasons, the observer sticks to neighborhoods of the angles and convex fragments of the boundary of $G$. The trajectory of $t$ is a curve $\mathcal{T}\subset Y$ with a given speed regime $v_t$ of the motion along it. The possibilities for the observer to track the object in a safe mode and for the object to avoid the observation depend on the positions of the observer and the object. We characterize the positions in which, for any $\mathcal{T}$, the object can choose a regime $v_t$ enabling the avoidance of observation and the positions guaranteeing that the observer can see a part of the trajectory.
Mots-clés : navigation, observer
Keywords: trajectory, moving object. 
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     author = {V. I. Berdyshev},
     title = {An object moving in $\mathbb R^2$ with a high-speed destructive miniobject and an unfriendly solid observer},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {76--82},
     year = {2020},
     volume = {26},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2020_26_4_a4/}
}
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V. I. Berdyshev. An object moving in $\mathbb R^2$ with a high-speed destructive miniobject and an unfriendly solid observer. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 26 (2020) no. 4, pp. 76-82. http://geodesic.mathdoc.fr/item/TIMM_2020_26_4_a4/

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